and \(d=1/2\)  is the element spacing normalized by the wavelength;
\(L_\mathrm {TX}\)  is the number of sub-paths in the TX-IRS channel;
\(\alpha _{\mathrm {TX},l}\) , \(\theta _{\mathrm {TX},l}\) , and \(\phi _{\mathrm {TX},l}\)  are the complex gain, the elevation angle of arrival (AOA), and the azimuth AoA of the \(l\) -th sub-path in the TX-IRS channel, respectively.
The parameters associated with the IRS-RX channel are defined similarly using the subscript “RX” and the term “angle of departure (AoD)".
In addition, we assume a block fading channel that the channel remains constant within a coherence interval [1]}.
